SOLUTION: prove that sin^6 theta = -1/32 (cos 6 theta - 6 cos 4 theta + 16 cos 2 theta - 10).

Algebra ->  Trigonometry-basics -> SOLUTION: prove that sin^6 theta = -1/32 (cos 6 theta - 6 cos 4 theta + 16 cos 2 theta - 10).      Log On


   

Question 1011603: prove that sin^6 theta = -1/32 (cos 6 theta - 6 cos 4 theta + 16 cos 2 theta - 10).
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!

It isn't true!  So instead of proving it, let's disprove it:

sin%5E6%28theta%29%22%22=%22%22

We'll just prove that it isn't true by substituting theta=0

sin%5E6%280%29%22%22=%22%22expr%28-1%2F32%29%28cos%286%2A0%29%5E%22%22+-+6cos%284%2A0%29+%2B+16cos%282%2A0%29+-+10%29

sin%5E6%280%29%22%22=%22%22expr%28-1%2F32%29%28cos%280%29%5E%22%22+-+6cos%280%29+%2B+16cos%280%29+-+10%29

sin(0) = 0 and cos(0) = 1, so

0%5E6%22%22=%22%22expr%28-1%2F32%29%281+-+6%281%29+%2B+16%281%29+-+10%29

0%22%22=%22%22expr%28-1%2F32%29%281+-+6+%2B+16+-+10%29

0%22%22=%22%22expr%28-1%2F32%29%281%29

0%22%22=%22%22-1%2F32

So that is false.  Did you perhaps copy it wrong?

Edwin